Partial regularity for a class of anisotropic variational integrals with convex hull property

Asymptotic Analysis

Volumn 32, Issue 3-4, 2002, Pages 293-315

  Bildhauer, M ^a   Fuchs, M ^a  

^a SAARLAND UNIVERSITY   (Germany)

Author keywords

Anisotropic growth; Minimizers; Regularity

Indexed keywords

EID: 0036972447     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. E. Acerbi and N. Fusco, Regularity for minimizers of non-quadratic functionals. The case 1 < p < 2, J. Math. Anal. Appl. 140 (1989), 115-135.
2. E. Acerbi and N. Fusco, Partial regularity under anisotropic (p,q) growth conditions, J. Differential Equations 107(1) (1994), 46-67.
3. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Science Publications, Clarendon Press, Oxford, 2000.
4. M. Bildhauer, A priori gradient estimates for bounded generalized solutions of a class of variational problems with linear growth, J. Convex Anal. 9 (2002), 117-137.
5. M. Bildhauer, Convex variational problems with linear, nearly linear and/or anisotropic growth conditions, Habilitations-schrift. Universität des Saarlandes, 2001.
6. M. Bildhauer and M. Fuchs, Partial regularity for variational integrals with (s, μ, q)-growth, Calc. Var. 13 (2001), 537-560.
7. M. Bildhauer and M. Fuchs, Twodimensional anisotropic variational problems, Calc. Var., to appear.
8. 1,α-estimates for (double) obstacle problems under nonstandard growth conditions, Z. Anal. Anwendungen 20 (2001), 959-985.
9. S. Campanato, Hölder continuity of the solutions of some non-linear elliptic systems, Adv. Math. 48 (1983), 16-43.
10. B. Dacorogna, Direct Methods in the Calculus of Variations, Applied Mathematical Sciences, Vol. 78, Springer, Berlin, 1989.
11. A. D'Ottavio, F. Leonetti and C. Musciano, Maximum principle for vector valued mappings minimizing variational integrals, Atti Sem. Mat. Fis. Univ. Modena (1998).
12. L. Esposito, F. Leonetti and G. Mingione, Higher integrability for minimizers of integral functionals with (p, q)-growth, J. Differential Equations 157 (1999), 414-438.
13. L. Esposito, F. Leonetti and G. Mingione, Regularity for minimizers of functionals with p-q growth, Nonlinear Differential Equations Appl. 6(1999), 133-148.
14. L.C. Evans, Quasiconvexity and partial regularity in the calculus of variations, Arch. Rational Mech. Anal. 95 (1986), 227-252.
15. I. Fonseca and J. Malý, Relaxation of multiple integrals below the growth exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), 309-338.
16. 1,α-regularity for free and constrained local minimizers of elliptic variational integrals with nearly linear growth, Manuscripta Math. 102 (2000), 227-250.
17. M. Fuchs and V. Osmolovski, Variational integrals on Orlicz-Sobolev spaces, Z. Anal. Anwendungen 17 (1998), 393-415.
18. M. Fuchs and G. Seregin, Variational models for fluids of Prandtl-Eyring type and plastic materials with logarithmic hardening. Math. Methods Appl. Sci. 22 (1999), 317-351.
19. M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. Math. Studies, Vol. 105, Princeton University Press, Princeton, 1983.
20. M. Giaquinta and G. Modica, Remarks on the regularity of the minimizers of certain degenerate functionals, Manuscripta Math. 57 ( 1986), 55-99.
21. P. Marcellini, Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions, Arch. Rational Mech. Anal. 105 (1989), 267-284.
22. P. Marcellini, Regularity and existence of solutions of elliptic equations with (p, q)-growth conditions, J. Differential Equations 90 (1991), 1-30.
23. P. Marcellini, Everywhere regularity for a class of elliptic systems without growth conditions, Ann. Scuola Norm. Sup. Pisa 23 (1996), 1-25.
24. M. Meier, Reguläre und singuläre Lösungen quasilinearer elliptischer Gleichungen und Systeme I, II, Preprint Bonn University/SFB 72 No. 245, 246, 1979.
25. 1,α regularity for minimizers of integral functionals with L log L growth, Z. Anal. Anwendungen 18 (1999), 1083-1100.
26. C.B. Morrey, Multiple Integrals in the Calculus of Variations, Grundlehren der Math. Wiss. in Einzeldarstellungen, Vol. 130, Springer, Berlin, 1966.
27. A. Passarelli Di Napoli and F. Siepe, A regularity result for a class of anisotropic systems, Rend. Ist. Mat. Univ. Trieste 28(1-2) (1996), 13-31.